[vtkusers] Re: Curvature in respect to size of surface

[Goodwin Lawlor]

Peter,

Sounds like you're looking for Koenderink's "Shape Index" and 
"Curvedness" - two functions of the principal curvatures which decouple 
shape and size respectively.

I'm sure a web search will shed more detail. Koenderink's book "Solid 
Shape" has probably the best explanation if you can get your hands on it.

hth

Goodwin

ps There's an example of Shape Index on my homepage 
http://www.bioengineering-research.com/

Boettcher, Dr. Peter wrote:
> vtkCurvature calculates the mean or gauss curvature of a surface. 
> However the interpretation what one would consider a considerable 
> curvature (been not flat) may depend on the size of the surface 
> considered. For example taking a 5 mm area of a 10 cm sphere would be 
> flat in average, in contrast to a 2 cm big area which will be convex. 
>  Currently I use the following approach. At each point of the surface I 
> clip the surface around that point of the diameter which I am interested 
> in. Than I measure the angle between the surface normal at the centre 
> and the surface normals at the other points of the clipped portion of 
> the surface. Finally the mean angle is calculated, representing the 
> deviation from been flat. A mean angle of 0 would mean the surface is 
> flat. Unfortunately this approach does not differentiate between concave 
> and convex and mixed surfaces.
> 
> Are there already established algorithms measuring the curvature in 
> respect to the size of the surface investigated?